Trim the green portions of the leek and tie 2 leek leaves, bay leaves, peppercorns and thyme together in a piece of cheesecloth or use a tea ball by placing all of the ingredients listed above into the ball. This is called a bouquet garni.
Using a sharp knife, halve the white part of the leek lengthwise and rinse well under cold running water to rid the leek of any sand. Slice thinly crosswise and set aside.
In a large soup pot over medium heat, melt the butter and add the bacon. Cook for 5 to 6 minutes, stirring occasionally, until the bacon is very soft and has rendered most of its fat. Add the chopped leeks and cook until wilted, about 5 minutes. Add the wine and bring to a boil. Add the reserved bouquet garni, chicken stock, potatoes, salt and white pepper, and bring to a boil. Reduce the heat to a simmer and cook for 30 minutes, or until the potatoes are falling apart and the soup is very flavorful.
Remove the bouquet garni and, working in batches, puree the soup in a food processor or blender. Stir in the heavy cream and adjust the seasoning, if necessary. Serve immediately, with some of the chopped chives sprinkled over the top of each bowl of soup.